David Cameron's government is accused of using the floods to "sneak" out bad news. Photograph: Pool/Reuters

David Cameron was accused of using the floods to "drown embarrassing news" after the government announced it is publishing a raft of reports on Britain's relationship with the EU, one of which concludes that the single market is vital to the UK economy.

In one of the most eye-catching findings of the eight volumes, easyJet says it would not exist were it not for the EU's single market.

The low cost airline told the review: "easyJet is a product of the EU's deregulation of Europe's aviation market. Without deregulation we would not exist."

The release of the documents has drawn criticism because Downing Street had issued an instruction earlier this week to every government department to hold back on any non-urgent announcements that are unrelated to the floods.

But in a written parliamentary answer, the foreign secretary William Hague will publish the reports in the latest instalment of the government's "balance of competences" review.

Mike Gapes, the Labour backbencher who led the charge in the Commons against a Tory private member's bill that would have established a referendum on Britain's EU membership by 2017, said the government was using the floods crisis to "sneak" out a report which hails the benefits of the EU.

Gapes said: "They're sneaking it out – this is a good day to drown embarrassing news. Given that parliament is going into recess for the half term next week they're sneaking it out so it can't be scrutinised with any discussion next week. There won't be a prime minister's questions next week."

The praise for the single market is made in one of eight reports – covering investment; the single market in goods; transport; environment; civil justice; asylum and immigration from outside the EU; culture media and sport; and research and development – compiled by civil servants.

Officials were tasked by the coalition with making a detailed assessment of EU regulations on Britain as part of a compromise after the Liberal Democrats blocked the Tories from repatriating powers from the EU after the election.

A government source said of the report on the single market: "There is a great weight of evidence that the single market is beneficial for our economy, for growth and job creation. It is a great force of liberalisation. Broadening and liberalising the single market further would be a boost to businesses and growth.

"On balance, not including agriculture, the EU's role in trade has been beneficial in liberalising international trade."

The findings will be a mixed blessing for Cameron. He is a strong supporter of the single market. But the strong praise in the report was seized on by pro-Europeans who fear that the prime minister is jeopardising Britain's relationship with the EU by pledging to hold an in/out referendum by 2017 with no guarantee that he will be able to renegotiate Britain's membership terms.

Douglas Alexander, the shadow foreign secretary, said: "Even before publication, it is clear that David Cameron's own balance of competences review has abjectly failed in one of its key purposes which was to try and temporarily unite a Tory party that today remains as divided as ever over Europe."

Roland Rudd, chairman of Business for New Europe said: "This clearly demonstrates how enormous the benefits of the single market really are: some huge firms would not even exist were it not for Britain's membership. What is so important in this debate is concrete evidence and this report shows just that: direct views from businesses who operate in the single market daily."

Adam Nathan, director of the pro-European British Influence Our Biggest Market campaign, said: "What is striking from the evidence is the strength of British economic interests in the maintenance and further development of the single market. easyJet is clear that it would not exist without opening of the single market for air transport. Businesses of all shapes and sizes want common regulations and standards for EU-wide production. Europe needs to be reformed, but it is clearly already doing many things right in terms of jobs and growth for the UK economy."

The reports also warn there is a problem with regulation. The government source said: "We have a problem with the stock and flow of regulation."

On transport and environment the reports highlights "widespread problems with EU regulation". The source said: "There is too much unnecessary interference, imposing unnecessary costs on business particularly for SMEs. There is too little evidence to support legislative action."

On borders, asylum, immigration, trade promotion and tourism the "weight of evidence is clear that more EU powers would be damaging". On civil justice Britain's opt-in, opt-out system is "crucial to protecting our criminal justice common law system". Tony Blair negotiated a system which allows Britain to opt out of all criminal just measures and then to negotiate on which measures to opt back into.

The report which examines the free movement of EU citizens within the EU has been delayed. Theresa May is pressing for a cap to be imposed – a proposal that is being resisted by the Liberal Democrats on the grounds that that would place Britain in breach of its EU obligation.